A Cloud ERP system means traditional ERP solutions hosted off-site. It is also flexible and scalable. The system has the capability to access real-time data from anywhere without using complicated and costly remote-access software.
On the other hand SaaS (Software-as-a-Service) model offerings are typically smaller. This is normally best for organizations with limited complexity, size and global presence. ERP system providers host SaaS on their own infrastructures instead of locating the systems on-premise at the purchasing organization.
In SaaS model, the vendor will have the full control of the application and not the customer where as in Cloud ERP system your data and your application can be placed on server that you control. Both these models provide instant gratification, taking mere minutes to be up and running.